Question 3 [12 marks] The following question requires you to solve for the optimal amount of time Jeff allocates to farming. Assume a model comprising of Jeff, a farmer, and Tom, a farm owner. JeF's preferences: We assume that Jeff has a quasilinear utility function: U(t,c) = 1:0?) + c = ax/E + c where t is hours leisure and c is grain and a is a parameter for which you will be given a value. Jef's production relationship: Assume grain production (y) by Jeff is represented by the following relationship: 3' = BU) = deGM - I) Where b and d are parameters for which you will be provided values. In the question below, you will be provided with values for a, b and d. Substitute these values into the above equations. Then complete the following questions, showing calculations, on a piece of paper or electronically on your computer. You will be required to load up your nal results. Assume: a=14,b=7,d=2 Lera=20.b=l'0.d=2 a. [1 point) Calculate Jeff's Marginal Utility of free-time when he is spending 5 hours of leisure. b. (1 point) Calculate Jeff's Marginal Utility of grain (cl when he is consuming 15 grain. (1 point) Calculate Jeff's Marginal rate of substitution when he is spending 5 hours of leisure and consuming 15 grain. d. (1 points) How much free-time is Jeff willing to give up for an additional unit of grain when he is spending 5 hours of leisure and consuming 10 grain? e. [1 points) How does Jeff's Marginal Rate of Substitution change as he increases free-time, holding grain consumption constant? Explain why you find this behaviour. f. (1 point) How does Jeff's Marginal Rate of Substitution change as he increases grain consumption, holding consumption of free-time constant? (1 points] Calculate the Marginal Rate of Transformation when Jeff works 18 hours on the farm. (2 points} Assume Jeff owns the farm. Calculate how many hours (h) he will work on the fa rm. i. [2 points) Now assume Tom owns the farm and Jeff has to pay rent of 6 grain to use the farm. :70.\" Calculate how much grain Jeff will consume. j. (1 points} Assume that Jeff has take-it-or-leave-it bargaining power. How much grain will Jeff consume